Solve for $x$ and $y$ using elimination. ${-2x-3y = -31}$ ${5x+3y = 37}$
Solution: We can eliminate $y$ by adding the equations together when the $y$ coefficients have opposite signs. Add the equations together. Notice that the terms $-3y$ and $3y$ cancel out. $3x = 6$ $\dfrac{3x}{{3}} = \dfrac{6}{{3}}$ ${x = 2}$ Now that you know ${x = 2}$ , plug it back into $\thinspace {-2x-3y = -31}\thinspace$ to find $y$ ${-2}{(2)}{ - 3y = -31}$ $-4-3y = -31$ $-4{+4} - 3y = -31{+4}$ $-3y = -27$ $\dfrac{-3y}{{-3}} = \dfrac{-27}{{-3}}$ ${y = 9}$ You can also plug ${x = 2}$ into $\thinspace {5x+3y = 37}\thinspace$ and get the same answer for $y$ : ${5}{(2)}{ + 3y = 37}$ ${y = 9}$